Seminar on Banach and Metric Space Geometry

Date: January 30, 2015

Time: 3:00PM - 4:00PM

Location: BLOC 220

Speaker: Quentin Menet, Université de Mons

Title: Hypercyclic subspaces

Abstract: An operator T on a Banach space X is said to be hypercyclic if there is a vector x in X (also called hypercyclic) whose the orbit under T is dense. An important question about hypercyclic operators is to know if there exists an infinite-dimensional closed subspace in which every non-zero vector is hypercyclic for T. Such a subspace is called a hypercyclic subspace. After a state of the art about hypercyclic operators and the structure of the set of hypercyclic vectors, we will see how we can obtain a characterization of weighted shifts with hypercyclic subspaces.